Solve 2(p-3)-(p-6)

$$2 ( p - 3 ) - ( p - 6 )$$

Evaluate

$$p$$

Solution Steps

Use the distributive property to multiply 2 by p-3.

$$2p-6-\left(p-6\right)$$

To find the opposite of p-6, find the opposite of each term.

$$2p-6-p-\left(-6\right)$$

The opposite of -6 is 6.

$$2p-6-p+6$$

Combine 2p and -p to get p.

$$p-6+6$$

Add -6 and 6 to get 0.

$$p$$

Differentiate w.r.t. p

$$1$$

Steps Using Definition of a Derivative

Use the distributive property to multiply 2 by p-3.

$$\frac{\mathrm{d}}{\mathrm{d}p}(2p-6-\left(p-6\right))$$

To find the opposite of p-6, find the opposite of each term.

$$\frac{\mathrm{d}}{\mathrm{d}p}(2p-6-p-\left(-6\right))$$

The opposite of -6 is 6.

$$\frac{\mathrm{d}}{\mathrm{d}p}(2p-6-p+6)$$

Combine 2p and -p to get p.

$$\frac{\mathrm{d}}{\mathrm{d}p}(p-6+6)$$

Add -6 and 6 to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}p}(p)$$

The derivative of ax^{n} is nax^{n-1}.

$$p^{1-1}$$

Subtract 1 from 1.

$$p^{0}$$

For any term t except 0, t^{0}=1.

$$1$$